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Laser-based additive manufacturing (AM) of glass is rare and complex, which involves highly non-linear thermodynamic problems. The temperature gradient is essential in analyzing the residual stress distribution and thermal deformation. At present, there is no accurate formula to describe the temperature field, and it is also difficult to measure the real-time temperature of the molten pool during the AM process. The numerical method in predicting the temperature field of fused silica glass laser becomes attractive. In this work, a finite element (FE) model for laser AM of quartz glass is established, and the temperature field of laser AM of quartz glass based on the principle of coaxial powder feeding is simulated by combining a moving heat source and birth-death element method. The temperature fields under different laser powers and scan speeds are investigated respectively. Results show that the peak temperature increases with the decrease of laser scan speed and the increase of laser power; The temperature of the upper layer is higher than that of the lower layer because of the heat accumulation effect; The increment rate of laser power and scan speed is set in the range of - 12.5% to 37.5% to ensure the temperature of AM region is slightly above the melting point of quartz glass. It is found that the influence of power change on the temperature field is more significant than that of scanning speed. Meanwhile, the peak temperature-dependent linearly on those two variables disused. The results provided here are instructive for subsequent laser AM of glass material including coaxial powder feeding method, powder cladding, etc.